Interval analysis for uncertain aerodynamic loads with uncertain-but-bounded parameters

Abstract

In this paper, we make the first effort to apply the interval method to aerodynamic loads analysis considering uncertainty in the case of insufficient sample data, and the effectiveness of this method is validated. The interval perturbation method and subinterval perturbation method are extended to evaluate the uncertain aerodynamic loads region with uncertain-but-bounded parameters. The uncertain parameters with insufficient information are quantified as interval variables. By combining the vortex lattice method and the interval theory, the interval aerodynamic model which is applicable to the subsonic regime is constructed. The first-order Taylor expansion and first-order Neumann series are employed to calculate the response intervals of lift coefficients. Based on the subinterval theory, the subinterval perturbation method for the interval aerodynamic model is developed to solve the aerodynamic problems with large uncertainty level. Two numerical examples for wing models, which consider uncertainty in incoming flow conditions and geometry, are given to validate the feasibility and effectiveness of the proposed methods by comparing the results with Monte Carlo simulations. Moreover, the present methods are extended to evaluate the uncertainty propagation in the pitching moment coefficient and induced drag coefficient.